Krovinovic, 24, had a fine season on loan with the now-promoted Baggies, making 25 starts in all competitions.
But according to Record in Portugal, they only want to pay €10m (£9m) to make his stay permanent.
That is considerably less than Benfica’s valuation of the Croat, and with no fixed option to buy in the loan deal, the clubs must negotiate.
Benfica are undergoing a revolution led by returning coach Jorge Jesus, meaning some players must go.
Krovinovic, who struggled for regular game time following his €3m move from Rio Ave in 2017, is one of those likely to leave.
Perhaps knowing this, West Brom are trying to haggle his price down, with €10m said to be their limit.